ws 7 lineaire trend

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 27 Nov 2009 11:35:28 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/27/t1259346980atdnvucovnaawbk.htm/, Retrieved Fri, 27 Nov 2009 19:36:31 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Nov/27/t1259346980atdnvucovnaawbk.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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2.7 0 2.3 0 1.9 0 2.0 0 2.3 0 2.8 0 2.4 0 2.3 0 2.7 0 2.7 0 2.9 0 3.0 0 2.2 0 2.3 0 2.8 0 2.8 0 2.8 0 2.2 0 2.6 0 2.8 0 2.5 0 2.4 0 2.3 0 1.9 0 1.7 0 2.0 0 2.1 0 1.7 0 1.8 0 1.8 0 1.8 0 1.3 0 1.3 0 1.3 1 1.2 1 1.4 1 2.2 1 2.9 1 3.1 1 3.5 1 3.6 1 4.4 1 4.1 1 5.1 1 5.8 1 5.9 1 5.4 1 5.5 1 4.8 1 3.2 1 2.7 1 2.1 1 1.9 1 0.6 1 0.7 1 -0.2 1 -1.0 1 -1.7 1 -0.7 1 -1.0 1

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Inflatie[t] = + 3.39672949800379 + 2.17650224345689Kredietcrisis[t] -0.0659395248380129t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 3.39672949800379 0.440715 7.7073 0 0 Kredietcrisis 2.17650224345689 0.740438 2.9395 0.004741 0.002371 t -0.0659395248380129 0.02127 -3.1001 0.003005 0.001502 Multiple Linear Regression - Regression Statistics Multiple R 0.384504831834612 R-squared 0.147843965704164 Adjusted R-squared 0.117943753974485 F-TEST (value) 4.94457922374563 F-TEST (DF numerator) 2 F-TEST (DF denominator) 57 p-value 0.0104663444822474 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.44732736739507 Sum Squared Residuals 119.401120979413 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.7 3.33078997316579 -0.630789973165794 2 2.3 3.26485044832777 -0.96485044832777 3 1.9 3.19891092348976 -1.29891092348976 4 2 3.13297139865174 -1.13297139865174 5 2.3 3.06703187381373 -0.76703187381373 6 2.8 3.00109234897572 -0.201092348975718 7 2.4 2.93515282413770 -0.535152824137705 8 2.3 2.86921329929969 -0.569213299299692 9 2.7 2.80327377446168 -0.103273774461678 10 2.7 2.73733424962367 -0.0373342496236655 11 2.9 2.67139472478565 0.228605275214347 12 3 2.60545519994764 0.39454480005236 13 2.2 2.53951567510963 -0.339515675109627 14 2.3 2.47357615027161 -0.173576150271614 15 2.8 2.4076366254336 0.392363374566399 16 2.8 2.34169710059559 0.458302899404412 17 2.8 2.27575757575758 0.524242424242424 18 2.2 2.20981805091956 -0.00981805091956223 19 2.6 2.14387852608155 0.456121473918451 20 2.8 2.07793900124354 0.722060998756463 21 2.5 2.01199947640552 0.488000523594476 22 2.4 1.94605995156751 0.453940048432489 23 2.3 1.88012042672950 0.419879573270502 24 1.9 1.81418090189148 0.085819098108515 25 1.7 1.74824137705347 -0.048241377053472 26 2 1.68230185221546 0.317698147784541 27 2.1 1.61636232737745 0.483637672622554 28 1.7 1.55042280253943 0.149577197460567 29 1.8 1.48448327770142 0.31551672229858 30 1.8 1.41854375286341 0.381456247136592 31 1.8 1.35260422802539 0.447395771974605 32 1.3 1.28666470318738 0.0133352968126182 33 1.3 1.22072517834937 0.0792748216506311 34 1.3 3.33128789696824 -2.03128789696824 35 1.2 3.26534837213023 -2.06534837213023 36 1.4 3.19940884729222 -1.79940884729222 37 2.2 3.1334693224542 -0.933469322454203 38 2.9 3.06752979761619 -0.167529797616191 39 3.1 3.00159027277818 0.0984097272218226 40 3.5 2.93565074794016 0.564349252059835 41 3.6 2.86971122310215 0.730288776897848 42 4.4 2.80377169826414 1.59622830173586 43 4.1 2.73783217342613 1.36216782657387 44 5.1 2.67189264858811 2.42810735141189 45 5.8 2.6059531237501 3.1940468762499 46 5.9 2.54001359891209 3.35998640108791 47 5.4 2.47407407407407 2.92592592592593 48 5.5 2.40813454923606 3.09186545076394 49 4.8 2.34219502439805 2.45780497560195 50 3.2 2.27625549956004 0.923744500439965 51 2.7 2.21031597472202 0.489684025277978 52 2.1 2.14437644988401 -0.0443764498840096 53 1.9 2.07843692504600 -0.178436925045997 54 0.6 2.01249740020798 -1.41249740020798 55 0.7 1.94655787536997 -1.24655787536997 56 -0.2 1.88061835053196 -2.08061835053196 57 -1 1.81467882569395 -2.81467882569395 58 -1.7 1.74873930085593 -3.44873930085593 59 -0.7 1.68279977601792 -2.38279977601792 60 -1 1.61686025117991 -2.61686025117991 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0397389062672699 0.0794778125345399 0.96026109373273 7 0.0101274626392263 0.0202549252784526 0.989872537360774 8 0.00242591899741342 0.00485183799482685 0.997574081002587 9 0.000676909184028205 0.00135381836805641 0.999323090815972 10 0.000152502326904213 0.000305004653808425 0.999847497673096 11 3.80333144865629e-05 7.60666289731259e-05 0.999961966685514 12 8.7141382799589e-06 1.74282765599178e-05 0.99999128586172 13 8.90842890329621e-06 1.78168578065924e-05 0.999991091571097 14 3.47517583894201e-06 6.95035167788402e-06 0.999996524824161 15 7.68789499009676e-07 1.53757899801935e-06 0.9999992312105 16 1.55178306462206e-07 3.10356612924411e-07 0.999999844821694 17 2.92578360599061e-08 5.85156721198122e-08 0.999999970742164 18 2.22142571850941e-08 4.44285143701882e-08 0.999999977785743 19 4.39950081340599e-09 8.79900162681199e-09 0.9999999956005 20 8.30782996170599e-10 1.66156599234120e-09 0.999999999169217 21 1.85752334241883e-10 3.71504668483765e-10 0.999999999814248 22 4.87189893936008e-11 9.74379787872015e-11 0.99999999995128 23 1.50780825219303e-11 3.01561650438606e-11 0.999999999984922 24 2.06294004725406e-11 4.12588009450812e-11 0.99999999997937 25 3.52160492606124e-11 7.04320985212247e-11 0.999999999964784 26 1.07073070047285e-11 2.14146140094571e-11 0.999999999989293 27 2.34813294161743e-12 4.69626588323487e-12 0.999999999997652 28 1.24532869092981e-12 2.49065738185961e-12 0.999999999998755 29 3.63378418648588e-13 7.26756837297176e-13 0.999999999999637 30 9.01368017642594e-14 1.80273603528519e-13 0.99999999999991 31 1.98214901309529e-14 3.96429802619057e-14 0.99999999999998 32 1.59653809938100e-14 3.19307619876199e-14 0.999999999999984 33 7.89965842087368e-15 1.57993168417474e-14 0.999999999999992 34 6.02329403780188e-15 1.20465880756038e-14 0.999999999999994 35 1.01880775720702e-14 2.03761551441403e-14 0.99999999999999 36 4.26236391195322e-14 8.52472782390645e-14 0.999999999999957 37 1.37282842366875e-12 2.74565684733749e-12 0.999999999998627 38 2.79052022730219e-10 5.58104045460438e-10 0.999999999720948 39 3.2867348922477e-08 6.5734697844954e-08 0.999999967132651 40 4.40485651385031e-06 8.80971302770061e-06 0.999995595143486 41 0.00046392263597718 0.00092784527195436 0.999536077364023 42 0.0193435217654132 0.0386870435308264 0.980656478234587 43 0.328843663348304 0.657687326696608 0.671156336651696 44 0.762380110629254 0.475239778741492 0.237619889370746 45 0.873612387981203 0.252775224037595 0.126387612018797 46 0.894003988547132 0.211992022905735 0.105996011452868 47 0.873758312408006 0.252483375183987 0.126241687591994 48 0.907490025277145 0.18501994944571 0.092509974722855 49 0.947270639080012 0.105458721839977 0.0527293609199885 50 0.90914172395072 0.181716552098559 0.0908582760492795 51 0.85919402828293 0.281611943434141 0.140805971717070 52 0.793482543018373 0.413034913963255 0.206517456981627 53 0.796043553491189 0.407912893017622 0.203956446508811 54 0.690411777511897 0.619176444976207 0.309588222488103 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 34 0.693877551020408 NOK 5% type I error level 36 0.73469387755102 NOK 10% type I error level 37 0.755102040816326 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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